Scientific advances - whether in genetics, gene manipulation and propagation - have changed the breeding process and the transition to commercial production out of recognition. But the plant (or animal) still has to meet enough of the right criteria in the real world to be worthwhile.
There's something like 30,000 varieties of rose. A lot of the French ones bred 150 years ago remain gardenworthy. If you look at the hybrid teas / floribundas (or whatever these are now called) in the garden centre or on offer in the media, they are mostly varieties that were deservedly popular 50 years ago. Though plant breeder's rights may have something to do with that! The big developments are the strains of English / modern roses developed by David Austin, Graham Thomas and others which which produce roses that on the whole are more gardenworthy than most of the old varieties. But how many of those are really any better than the varieties they have already introduced? There's a Rose of the Year every season and I wonder how many of those have been successful sellers afterwards?
You see that most clearly with all the "fantastic new plants" on offer in the garden centres each spring and summer, in gaudy pots, mass produced and hyped up to hit the impulse buyer (guilty as charged). I bet you won't find any on sale anywhere the next year.
On the other hand, developments like surfinias are lasting because they are an improvement on petunias and meet a particular need well.
I suspect that climate change will have less effect on flowers than on vegetable breeding. Why spend time and money on adapting even a garden favourite when there are many other plants that will flourish that the public will buy instead?
Vegetables will be different, because there are fewer species and varieties in use and we are very dependent on some of them. We know that potatoes and tomatoes are being bred for resistance to blight which is difficult as blight itself mutates. If in the UK we will have more warm, wet blight-friendly summers, then we will need more of those new varieties soon (even if they are lacking in some other qualities). Runner beans and French beans are temperature / moisture sensitive too, will are current favourites suffice? And what will we do about windier weather which is predicted? Sometimes it may simply be a question of finding a related variety that grows in another part of the world in the sort of conditions we are heading for.
I'd also say that generally a good new variety of vegetable is "better" than the old varieties in general in some important way. That may be ease of commercial growing, processing and sale, such as more compact, heavier cropping plants, and it is not always taste (though that seems to be coming back in supermarket tomatoes and strawberries now). Heritage varieties are generally that for a reason - exhibit number 1 is stringy runner beans. I'm not saying that they shouldn't be preserved - the gene pool matters - but I'm not convinced they are the best thing for the family veg plot.
So I think we will soon see - and will need to see - some new varieties in our farms, allotments and gardens but that we will also grow more of some things that are less common or successful now.